Better approximation guarantee for Asymmetric TSP
Jens Vygen
TL;DR
This paper advances the approximation guarantees for the Asymmetric TSP, achieving ratios below 15, and improves bounds for related special cases and LP relaxations, contributing to more efficient solutions.
Contribution
It introduces improved approximation ratios for the Asymmetric TSP and related problems, along with tighter bounds on LP relaxation integrality ratios.
Findings
Approximation ratio for Asymmetric TSP less than 15
Improved ratios for unweighted digraphs and endpoint-constrained tours
Better upper bounds on LP relaxation integrality ratios
Abstract
We improve the approximation ratio for the Asymmetric TSP to less than 15. We also obtain improved ratios for the special case of unweighted digraphs and the generalization where we ask for a minimum-cost tour with given (distinct) endpoints. Moreover, we prove better upper bounds on the integrality ratios of the natural LP relaxations.
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Vehicle Routing Optimization Methods · Advanced Graph Theory Research